Second-half strikes from Andy Bell and substitute Adam Warlow gave Fleetwood victory over Leiston and secured them a second round tie at home to Hartlepool.
Bell bagged an inch perfect lob just three minutes into the second half to give the home side the lead.
Warlow settled the tie with 11 minutes remaining when he latched on to a Matty Kay pass and calmly slotted home.
Leiston sub Tes Bramble could have added an injury-time consolation but was denied by Fleet keeper Danny Hurst.
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